Question

Natalie can send or receive a text message for $0.15 or get an unlimited number for $5. Write and solve the inequality to find how many messages she can send and receive so the unlimited plan is cheaper than paying for each message

Answer 1

$33\frac{1}{3}$ number of messages she can send and receive so the unlimited plan is cheaper than paying for each message

Solution:

Natalie can send or receive a text message for $0.15

Natalie can get an unlimited number for $5

To find: Number of messages she can send and receive so the unlimited plan is cheaper than paying for each message

Let "x" be the number of messages

Cost for sending and receiving message = $ 0.15

Cost for unlimited plan = $ 5

Then, according to given, we frame a inequality as:

The condition is: unlimited plan is cheaper than paying for each message

Therefore,

(number of messages)(Cost for sending and receiving message) is greater than or equal to Cost for unlimited plan

$x \times 0.15\geq 5\\\\0.15x\geq 5\\\\\text{Solve for "x" }\\\\\text{Divide both sides of equation by 0.15 }\\\\\frac{0.15x}{0.15}\geq \frac{5}{0.15}\\\\x\geq 33.33\\\\x\geq 33\frac{1}{3}$

Thus for $33\frac{1}{3}$ messages ,the unlimited plan is cheaper than paying for each message